Ahmes Loaf Problem Reflection

 Our project was on Ahmes loaf, and I believe my group members and I worked well together in order to explain the problem and solution.

The loaf problem as discussed in the book was created as an extension and almost recreationally. This is quite how The Crest of Peacock discusses Babylonians. The problem is created to test the limits of solution and theory to see if it sustains. Does the behavior of a particular solution change and if it does then what are the boundaries of that. It is very informative about these questions such as the Ahmes loaf problem because it lets us know that exploring math abstractly is not a new concept for us. We could define application based on the logic and reasoning of the Ancient world with the problems they had, but they were just as curious as we are now. Like the Babylonians, they also did not have any references to build off on, and these application-based extensions are their method of exploring ideas.  

 

Regula Falsi is a false position method. It is an ancient method for solving an equation with one unknown. In a way, it's an assumption based and the simplest way to describe this trial-and-error method. When figuring out the hint of 5 ½ in Ahmes's solution, the book also mentioned that the origin of the 5 ½ is not clear. They applied and think Ahmes also applied n earlier method of Regula Falsi in order to come to the conclusion of 5 ½ being the difference. I too have used Regula Falsi, I can probably recall when I used trial and error to get to the answer in high school when I was not aware of a theory or axiom to follow. Regula Falsi is a great method to try and figure out patterns. For Ahmes' solution as the difference of 1 increases, the difference between the sum of the two lowest terms and 1/7 of the three largest terms decreases by 2/7. There is a relation between the increase of 1 to the difference of 2/7, thus there must be a number for which the difference is 0 and it is going to be figured out by how many times 2/7 goes into 1 2/7. Which gets us to the answer of 5 ½.

 

The process of this project has me comparing this to how we learn math when we are younger. Not to say that it is trivial in any sense, but when you are doing application questions, and you have multiple variations of the same topic, it is trying to make you understand the behavior of the solution. For example, when you are factoring and graphic equations, the increasing level of difficulty tests your knowledge, as you get to discover different cases. Abstract for me understanding the properties and behavior of a theory and object and application-based exploration is an excellent way to start thinking about math abstractly.